Question

Why $\mathbb{Q}(x_1,y_1,...,x_n,y_n)/\mathbb{Q}$ is a Galois extension? where $E[m]=\{(x_1,y_1),...,(x_n,y_n)\}$ is the m-torsion group.

score 98 · Answer 1 · 2026-03-25 07:45:39

98

Views

Why $\mathbb{Q}(x_1,y_1,...,x_n,y_n)/\mathbb{Q}$ is a Galois extension? where $E[m]=\{(x_1,y_1),...,(x_n,y_n)\}$ is the m-torsion group.

Published on 25 Mar 2026 - 7:45

score 42 · Answer 2 · 2026-03-30 02:05:42

42

Views

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score 85 · Answer 3 · 2026-03-30 02:06:50

85

Views

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score 232 · Answer 4 · 2020-05-01 22:19:54

232

Views

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score 107 · Answer 5 · 2026-03-25 07:44:55

107

Views

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score 966 · Answer 6 · 2026-03-25 22:10:44

966

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score 144 · Answer 7 · 2026-03-26 02:47:40

144

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score 92 · Answer 8 · 2026-03-25 07:45:42

92

Views

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score 76 · Answer 9 · 2026-03-25 07:44:46

76

Views

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score 66 · Answer 10 · 2026-03-28 11:34:21

66

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score 60 · Answer 11 · 2026-03-28 22:08:15

60

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score 93 · Answer 12 · 2026-03-25 19:04:06

93

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score 161 · Answer 13 · 2020-05-07 08:41:13

161

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100

Views

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score 83 · Answer 15 · 2020-05-07 16:55:26

83

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Published on 07 May 2020 - 16:55

List Question

Why $\mathbb{Q}(x_1,y_1,...,x_n,y_n)/\mathbb{Q}$ is a Galois extension? where $E[m]=\{(x_1,y_1),...,(x_n,y_n)\}$ is the m-torsion group.

Finding boundaries for a Diophantine equation

Why are the integral points on elliptic curve preserved under this substitution?

What is the solution of $\frac{x^3}{y^3+z^3}+\frac{y^3}{x^3+z^3}+\frac{z^3}{y^3+x^3}=1$ in rational?

$p^n$ power torsion and $p^{n+1}$ power torsion defined over the same field

How to use Lemniscate sine and Lemniscate cosine elliptic integrals?

Change of variables in the Weierstrass form $y^2=x^3+a_2x^2+a_4x+a_6$ for the generic fiber

Reference request for equivalence of reducibility of $\ell$-adic Galois representation and isogeny of degree $\ell$ on elliptic curve

Is the Galois condition necessary in order to define an action on an elliptic curve?

Question about the torsion group of an elliptic curve being cyclic

Rational independence of $j$-invariants

How to get group law of elliptic curve over $\mathbb{C}$ by Weierstrass $\wp$-function?

Rewriting elliptic curve with point of order 3

Multiplication by $n$ formula on elliptic curves

Question on Diophantine Equations

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